De Rham-Hodge decomposition and vanishing of harmonic forms by derivation operators on the Poisson space∗
نویسنده
چکیده
We construct differential forms of all orders and a covariant derivative together with its adjoint on the probability space of a standard Poisson process, using derivation operators. In this framewok we derive a de Rham-HodgeKodaira decomposition as well as Weitzenböck and Clark-Ocone formulae for random differential forms. As in the Wiener space setting, this construction provides two distinct approaches to the vanishing of harmonic differential forms.
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